1. Short-term Forecasting of Czech Quarterly GDP Using Monthly Indicators K. Arnoštová, D. Havrlant, L. Růžička and P. Tóth Macroeconomic Forecasting Division Monetary and Statistics Department Czech National Bank 11th of Oct, 2011

2. STF of GDP by MI Overview A.Motivation B.Tested models C.Data D.Results

3. A. Motivation Quarterly data of GDP – national accounts –published cca. 10 weeks after the end of the quarter A lot of monthly indicators are available (~70–100) –published early, i.e. end of a month or just a few weeks later Several models recently available in the literature can: –deal with mixed frequency data and unbalanced panels –condition the forecast on a large set of indicators –reduce forecast errors as opposed to univariate models A comprehensive study of recent short-term models for Czech GDP is missing. It is useful for forecasting at CNB.

4. B. Tested models We follow the ECB study Barhoumi etal. (2008): 1.Moving average (naive model) 2.NTF framework of CNB 3.Averaged bivariate VAR-sVAR 4.Bridge equationsBEQ 5.Static principal componentsPC 6.DFM ala Doz etal. 2007DFM 7.GDFM ala Forni etal. 2005GDFM

5. B. Tested models 1.Moving averages (naive model) average of last 4 quarters 2.Near-Term Forecasting (NTF) framework of CNB –GDP forecast = smoothed sum of expenditure components Note: GDP will be henceforth denoted as “y“

6. B. Tested models 3.Bivariate VAR-s quarterly aggregation of N indicators for all pairs of y and x i,t, i = 1..N we estimate a VAR(2,p i ) pairwise GDP forecasts are averaged

7. B. Tested models 4.Bridge equations (BEQ) quarterly aggr. of forecasted x-s (H=3h) BEQ for all pairs i of N pairwise GDP forecasts are averaged

8. B. Tested models 5.Static principal components (PC) estimation of static factors (PC) quarterly aggregation of factors forecasting GDP (OLS) „bridging with factors“

9. B. Tested models 6. Alternative principal components (PC-Q) Differs from PC in three ways: –PCs estimated on the quarterly aggregates –# of static factors is selected by the Kaiser criterion (PC eigenvalues > 1) –Incomplete quarters of monthly indicators are simply omitted

10. B. Tested models 7. DFM ala Doz etal. 2007 a)we estimate static factors by principal components, number of factors based on Bai and Ng (2002) b)we estimate the parameters of dyn. factors by OLS (number of dyn. factors based on Bai and Ng) c)given parameters from the previous step, we estimate dynamic factors and idiosyncratic terms by Kalman filter (flexible assumptions on the idiosyncratic terms) d)we aggregate forecasted factors to quarterly freq.: f Q t e)we regress y t+h on f Q t+h by OLS (on quarterly data; h is the forecast horizon)

11. B. Tested models 7. DFM ala Doz etal. 2007 estimate static factors (PC) estim. & forecast dyn. factors (KF) quarterly aggreg. of factors (H=3h) forecasting GDP (OLS) „bridging with factors“

12. B. Tested models 8. One-sided GDFM ala Forni etal. 2005 a)monthly indicators are aggregated to quarterly frequency (balancing by EM algorithm) b)GDFM is estimated on the combined database of quarterly indicators and GDP (max. no. of dyn. and stat. factors fixed, actual numbers selected by information criteria of Bai and Ng) c)GDP forecast is derived directly from the factor model as the forecast of common components

13. B. Tested models 8. One-sided GDFM ala Forni etal. 2005 quarterly aggregation of indicators y is GDP estimate GDFM on quarterly data forecast (z 1 = y = GDP)

14. C. Data Monthly indicators (98 series): –Industry, construction and services (43) –Labour market (5) –Foreign trade (4) –Price data (11) –Financial indicators (19) –Czech confidence indicators (6) –Foreign leading indicators (9) –Czech electricity consumption (1) Adjustment of GDP and monthly data: –Seasonal adjustment, quarterly growth rates –Some of monthly indicators further differenced to achieve stationarity

15. C. Data Indicator pre-selection – our rule of thumb: Used only for large-scale models (5.-8.) Goal: focus on indicators with most relevant information for GDP when estimating factor models Include if abs(corr.) with GDP growth > 0.5 If abs(corr.) between any two indicators is > 0.9, only the one more correlated with GDP is kept From the full set of 98 only 27 series survive Result: reduced forecast errors for models 5.,7.,8.

16. C. Data

17. D. Results Time interval:2001:q1 – 2009:q4 Evaluation interval: 2005:q1 – 2009:q4 Forecast horizon:1 to 3q ahead Number of indicators: up to 27 (98)

18. D. Results The smallest RMSE overall: PC Smallest RMSE 1Q ahead: NTF of CNB Note: relative RMSE is calculated vis-à-vis the RMSE of the moving average model

19. D. Results

20. Ranks: model ranking based on RMSE, out of the 7 main models + 4 additional models listed in the table above Relative rank, for example: = rank of PC – rank of PC full panel

21. Diebold-Mariano Test Statistic for the H0 of Equal Squared Forecast Errors

22. D. Results Results of the ECB study Countries: 7 of the eurozone Time period:1991:q1 – 2005:q3 Evaluation period: 2000:q1 – 2005:q3 Forecast horizon1 to 3q ahead Number of indicators: 76 - 393 by country RMSE vis-à-vis the naive model:

23. D. Results Results of the ECB study Countries: LT, HU, PL Time period:1995:q1 – 2005:q3 Evaluation period: 2002:q1 – 2005:q3 Forecast horizon:1 to 3q ahead Number of indicators: 80 – 103 by country RMSE vis-à-vis the naive model:

24. D. Results On CZ data, most models are more accurate than the naive model PC performs best overall, thus it is a good idea to condition the forecast on “many” but relevant monthly series Expert forecast (NTF) did at least as well as the best model (PC) 1Q ahead Factor models did quite well overall (PC and DFM better than VAR and BEQ) Factor models improved in precision if the indicator set was reduced to the most relevant subset Looking at errors of PC and PC-Q, timeliness of information is key Results (model rankings) are not quite generalizable across countries

25. Questions